The confocal fluorescent microscope directly eliminates the light emitted from out-of-focus internal structures. This has enabled the observation of fluorophore-labeled processes or 3D structures deep within thick specimens. Unfortunately, high performance objective lenses are designed for immersion fluids, such as oil, glycerol, or water; the index of the specimen must match these options closely. Correction collars can correct for spherical aberration at specific depths; however the adjustments are not practical using the popular technique of automated 3D optical sectioning. The quality of the research on thick "in-vivo" tissues, or living cellular cultures is compromised; it is especially severe in neurobiology because neural structures within tissues are large. The refractive index mismatch induces spherical aberration just a few microns beneath the cover-glass, and increases dramatically upon focusing deeper into the specimen; hundreds of microns for neurobiology. This aberration impairs the fluorescence images (1 or multiple-photon) in several serious ways: As the focal plane extends deeper into specimen, the image intensity diminishes dramatically, significant geometric distortions are induced in the axial direction, and, the resolution (especially axial) is strongly reduced. The depth of observation and the quantitative value of the fluorophore distribution are limited. Deconvolution is a widely-used, software algorithm that "inverts" the impact of the optical system. It recalculates the un-blurred image and produces a quantitatively valid fluorophore intensity distribution using the point spread function, or PSF. The PSF is derived from images of sub-resolved fluorescent beads, or deduced from the characteristics of the image itself using the "blind" algorithm. AutoQuant is a leading supplier of deconvolution software used for biomedical wide-field and confocal fluorescent microscopy. The basic theory and principles behind existing deconvolution algorithms require a constant PSF. Existing deconvolution technology is unable to fully restore images with depth-dependent spherical aberration. We propose a new approach to deconvolution that bypasses the usual spatial invariance requirement for the PSF. The development of these new algorithms will restore the resolution, geometric integrity, and intensity validity to 3D confocal fluorescent microscopy for thick specimens. We expect the proposed algorithms will be sufficiently practical to be incorporated as an add-on to our existing software deconvolution and visualization products. We will test this technology on images of neural structures in thick tissues. [unreadable] [unreadable] [unreadable]